Local-global principle for certain biquadratic normic bundles

• Autorzy: Yang Cao , Yongqi Liang
• Języki publikacji: EN

Abstrakty

EN

Let X be a proper smooth variety having an affine open subset defined by the normic equation $N_{k(√a,√b)/k}(x) = Q(t₁,..., tₘ)²$ over a number field k. We prove that: (1) the failure of the local-global principle for zero-cycles is controlled by the Brauer group of X; (2) the analogue for rational points is also valid assuming Schinzel's hypothesis.

Kategorie tematyczne

• 11G35: Varieties over global fields
• 14D10: Arithmetic ground fields (finite, local, global)
• 14G05: Rational points
• 14C25: Algebraic cycles
• 14G25: Global ground fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 164
• Numer: 2
• Strony: 137-144

Daty

wydano

2014

Twórcy

autor

Yang Cao

• School of Mathematical Sciences, Capital Normal University, 105 Xisanhuanbeilu, 100048 Beijing, China

autor

Yongqi Liang

• Institut de Mathématiques de Jussieu, - Paris Rive Gauche, Université Paris Diderot - Paris 7, Bâtiment Sophie Germain, 75013 Paris, France

Identyfikatory

DOI

10.4064/aa164-2-3